Carbon Nanocone: An Excellent Thermal Rectifier

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Carbon Nano-cone An Excellent Thermal Rectifier

• Nuo YANG (??)
• Department of Physics and
• Centre for Computational Science Engineering
• National University of Singapore

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Acknowledgement

• Collaborators
• Professor Dr. Baowen LI
• National University of Singapore.
• NUS Graduate School for Integrative Sciences and
  Engineering.
• Dr. Gang ZHANG
• Institute of Microelectronics, Singapore

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Outline

• Introduction
• Thermal rectifier
• Carbon Nano-cone
• Model Method
• Results and Explanations
• Conclusion

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Introduction

• Electrical rectifiers and transistors changed our
  life
• Phononics (thermal) devices
• phonon is used to carry and process information
• broad applications for heat control/management
• energy saving
• Thermal Rectifier plays the most central role in
  phononics devices

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• Theory Models of Thermal Rectifier
• Morse on-site potential
• Controlling the Energy Flow in Nonlinear
  Lattices A Model for a Thermal Rectifier, M.
  Terraneo, M. Peyrard, and G. Casati, Phys. Rev.
  Lett., 88, 094302 (2002).
• Frenkel-Kontorova (FK) Model,
• Thermal Diode Rectification of Heat Flux, B. Li,
  L. Wang, and G. Casati, Phys. Rev. Lett. 93,
  184301 (2004).
• FK Fermi-Pasta- Ulam (FPU) Model,
• Interface Thermal Resistance between Dissimilar
  Anharmonic Lattices, B. Li, J. Lan, and L. Wang,
  Phys. Rev. Lett. 95, 104302 (2005).
• FK Model
• Asymmetric Heat Conduction in Nonlinear Lattices,
  B. Hu, L. Yang, and Y. Zhang, Phys. Rev. Lett.,
  97, 124302 (2006).

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J

• A Graded Mass Chain with FPU
• Thermal rectification and negative differential
  thermal resistance in lattices with mass
  gradient, N. Yang, N. Li, L. Wang and B. Li,
  Phys. Rev. B 76, 020301(R) (2007)
• Conclusion for Theory Models of Thermal Rectifier
• High the rectifications R 100,000
• Difficult to achieve experimentally
• Length dependence

J-
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• Carbon Nanotube Thermal Rectifier
• The first solid-state thermal rectifier, carbon
  or boron nitride nanotubes with non-uniform axial
  mass distribution, was reported experimentally by
  C. W. Chang, D. Okawa, A. Majumdar, and A. Zettl.
  a
• G. Wu and B. Li also studied the rectification in
  carbon nanotube junctions by using molecular
  dynamics method. b
• However, the rectifications ( 7 for a and
  20 for b) limit the application of the
  nanotube thermal rectifier.
• Results in b showed the rectification was
  dependent on the length of nanotube

a C. W. Chang, D. Okawa, A. Majumdar, and A.
Zettl, SCIENCE, 314, 1121 (2006). b G. Wu and
B.Li, Phys. Rev. B 76, 085424 (2007).
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• Carbon nano-cone
• Observed by Maohui Ge and Klaus Sattler,1994.a
• Characterized by cone angle, five possible angles
  are 19, 39, 60, 85 and 113 degrees b
• High Asymmetry in geometry
• Semiconductor c

a M. Ge and K. Sattler, Chem. Phys. Lett., 220,
192 (1994) b T. W. EBBESEN, Acc. Chem. Res.,
31, 558-566 (1998) c J.-C.Charlier and G.-M.
Rignanese Phys. Rev. Lett., 86, 5970 (2001).
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Model Method

• Classical molecular dynamics simulations used
• No. of Atoms 2,577 20,155
• A Morse bond and a harmonic cosine angle for C-C
  bonding interaction, which include both two-body
  and three-body potential terms a
• Nosé-Hoover heat bathes are used
• The heat flux is defined as the energy
  transported along the surface in unit time b
• where is ei local site energy, Fij is two-body
  force, and Fj(ijk) is three-body force

a R. E. Tuzun, D. W. Noid , B. G. Sumpter, and
R. C. Merkle, Nanotech. 7 (3), 241-248. (1996)
b P. K. Schelling S. R. Phillpot and P.
Keblinski, Phys. ReV. B, 65, 144306 (2002).
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Results and Explanations
Figure. (a) Rectifications for the homogenous
mass carbon nanocone. (b) Heat flux J versus ?.
(c) Temperature Profile of nanocone for ?
0.5. Here, N40, and T0300 K.
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The factors which affect the rectifications

• Temperature effect

Figure (a) and (b) Rectifications and heat fluxes
of carbon nanocone at different temperature, T0,
with fixed N40 layers and ? 0.5.
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• Size independence

Figure. (c) and (d) Rectifications and heat
fluxes for different length of carbon nanocone,
with fixed T0 300K, and . Here N changes from 20
layers to 100 layers . The rectification is about
100.
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Mechanics
Figure. Phonon Spectra of atoms in layers close
to the top and bottom. (a) and (b) T050K Upper
panel, the bottom heat bath is at high
temperature (?0.5) which corresponds to big heat
flux. Lower panel, ? -0.5 which corresponds to
small heat flux.
J. Shiomi and S. Maruyama, Non-Fourier heat
conduction in a single-walled carbon nanotube
Classical molecular dynamics simulations, Phys.
Rev. B, 73, 205420 (7 pages), (2006).
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Figure. Phonon Spectra of atoms in layers close
to the top and bottom. (a) and (b) T050K (c)
and (d) T0300K Upper panel, the bottom heat
bath is at high temperature (?0.5) which
corresponds to big heat flux. Lower panel, ?
-0.5 which corresponds to small heat flux.
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Conclusion

• An excellent thermal rectifier realized with
  carbon nanocone is proposed.
• Temperature effect and length independence are
  shown.
• Physical mechanism for the carbon nanocone
  thermal diode is understood by the match/mismatch
  phonons DOS spectra.

Thanks